1. Field of the Invention
The present invention is directed in general to nuclear magnetic resonance tomography (also called magnetic resonance imaging—MRI) as employed in medicine for examining patients. The present invention is particularly directed to a magnetic resonance tomography apparatus as well as to a method for the operation thereof wherein the technique referred to as partially parallel acquisition (PPA) is employed.
2. Description of the Prior Art
MRI is based on the physical phenomenon of nuclear magnetic resonance and has been successfully utilized as an imaging method in medicine and in biophysics for more then fifteen years. Given this examination method, the subject is subjected to a strong, constant magnetic field. As a result, the nuclear spins of the atoms in the subject, that were previously irregularly oriented, are aligned. Radio-frequency pulses can then excite these “ordered” nuclear spins to a specific resonance. This resonance generates the actual measured signal in MRI that is registered with suitable reception coils. By utilizing non-uniform magnetic fields generated by gradient coils, the test subject can be spatially encoded in all three spatial directions. The method allows a free selection of the slice to be imaged, and as a result tomograms of the human body can be registered in all directions. MRI has a tomographic method in medical diagnostics is mainly distinguished as a “non-invasive” examination method with versatile contrast capability. Due to the excellent presentation of the soft tissue, MRI has developed to a method that is often superior to x-ray computed tomography (CT). MRI is currently based on the application of spin echo sequences and gradient echo sequences that enable an excellent image quality with measurement times on the order of magnitude of minutes.
Constant technological improvement of components of MRI apparatuses and the introduction of fast imaging sequences have increased the areas of employment in medicine for MRI. Real-time imaging for supporting minimally invasive surgery, functional imaging in neurology and profusion measurement in mapiology are only a few examples. Despite the technical progress in the construction of MRI apparatuses, the exposure time of an MRI image remains the limiting factor for many applications of MRI in medical diagnostics. Further enhancement in the performance of MRI apparatus is limited from a technical point of view (feasibility) and for reasons of patient protection (stimulation and tissue heating). In recent years, many efforts have therefore been undertaken to develop and to establish new approaches in order to achieve further shortening in the image measuring time.
One approach for shortening the acquisition time is to reduce the number of image data to be registered. In order to obtain a complete image from such a reduced data set, either the missing data must be reconstructed with suitable algorithms or the faulty image must be corrected from the reduced data. The registration of the data in MRI occurs in k-space (synonym: frequency domain). The MRI image in the image domain is linked by Fourier transformation with the MRI data in k-space. The location encoding of the subject that defines k-space occurs with gradients in all three spatial directions. A distinction is made between the slice selection (determines an exposure slice in the subject, usually the z-axis), the frequency encoding (defines a direction in the slice, usually the x-axis) and the phase encoding (determines the second dimension within the slice, usually the y-axis). Without limitation to universal applicability, a Cartesian k-space is assumed below, this being sampled line-by-line. The data of an individual k-space row are frequency-encoded upon readout with a gradient. The row in the k-space has the spacing Δky that is generated by a phase encoding step. Since the phase encoding consumes much time compared to other location encodings, most methods for shortening the image measuring time are based on a reduction of the number of time-consuming phase encoding steps. All methods referred to as partially parallel acquisition, abbreviated as PPA below, are based on the above principle.
The basic idea in PPA imaging is that k-space data are registered not by an individual coil but, for example, by a linear arrangement of component coils, a coil array. Each of the spatially independent coils of the array carries certain spatial information that is utilized in order to achieve a complete location encoding by a combination of the simultaneously acquired coil data. This means that a number of omitted lines shifted in k-space can be determined from a single, registered k-space row.
The PPA methods thus employ spatial information that are contained in the components of a coil arrangement in order to partially replace the time-consuming phase encoding, which is normally generated using a phase encoding gradient. As a result, the image measuring time corresponding to the ratio of a number of lines of the reduced data set relative to the number of lines of the conventional data set (i.e., a complete data set) is reduced. In a typical PPA acquisition, only a fraction (½, ⅓, ¼, etc.) of the phase encoding lines is acquired compared to the conventional acquisition. A specific reconstruction is then applied to the data in order to reconstruct the missing k-space rows, and thus to obtain the complete field of view (FOV image in a fraction of the time).
Whereas some of these PPA techniques (SMASH, SENSE, GSMASH, which are described in brief below) have been successfully employed in many areas of MRI —SMASH and SENSE must be given priority—, the most significant disadvantage of these methods is that the complex sensitivity of every individual component coil must be exactly known. This is frequently problematical in practice since the experimental determination of the coil sensitivities is greatly hindered due to disturbances as a result of noise and—even more important—due to spin density fluctuations in the tissue, and thus leads to error-affected reconstructions. It is specifically this problem that still restricts a widespread clinical application of PPA methods.
First, the SMASH method invented by Sodickson in 1997 shall be described (D. K. Sodickson, W. J. Manning, Simultaneous Acquisition of Spatial Harmonics (SMASH): Fast Imaging with Radiofrequency Coil Arrays, Magn. Reson. Med. 38:591-603 (1997)). SMASH stands for “SiMultaneous Acquisition of Spatial Harmonics”. As mentioned above, this is a PPA method. Data are simultaneously acquired from spatially separate and independent coils that are arranged in phase encoding direction. By linear combination of these coil data, a spatial modulation of the signal is achieved, this having been achieved in conventional methods by the switching of a phase encoding gradient, as a result of which time-consuming phase encoding steps are eliminated. Only a reduced k-space thus is registered; the registration time is shortened corresponding to the reduction of this k-space. The missing data are then reconstructed after the actual data acquisition by suitable linear combinations of the coil data sets.
Sodickson et al thus showed that a row of k-space can be reconstructed by employment of linear combinations of signals acquired by an arrangement of coils according to the SMASH technique when the following always applies:                                           ∑                          l              =              1                        L                    ⁢                                    n              l                              (                m                )                                      ⁢                                          C                l                            ⁡                              (                y                )                                                    =                              C            0                    ⁢                                    ⅇ                              ⅈ                ⁢                                                                   ⁢                m                ⁢                                                                   ⁢                Δ                ⁢                                                                   ⁢                                  k                  y                                                      .                                              (        1        )            The quantity C0 is a phase-corrected sum of the individual coil sensitivities; in the idealized case, this constant would be equal to one over the entire region. The exponential term describes a sinusoidal modulation of the real part and the imaginary part. The number of oscillations of this modulation over the FOV is determined by the number m. The designation m=0, 1, 2, . . . , mean the spatial harmonic of the zero-th, first, second, . . . order of the coil sensitivities.
The quantity Cl(y) is the coil sensitivity of the coil l of a total of L coils. Further, n1(m)SMASH weighting factors are required for the linear combination of the coil sensitivities in order to generate spatial harmonics of the order m. The coil sensitivity profiles Cl(y) are normally determined by a separate acquisition using a proton density-weighted FLASH or similar sequence. When the coil sensitivities are known, the spatial harmonics can be calculated in purely mathematical form therewith. The weighting factors n1(m)) thus remain as the only unknown quantity in Equation (1). The determination of these coefficients is implemented such that the coil sensitivity profiles are fitted to the profiles of the spatial harmonics. With the assistance of these coil weighting factors, different lines can now be reconstructed from a single, acquired line; this is established by                               S          ⁡                      (                                          k                y                            +                              m                ⁢                                                                   ⁢                Δ                ⁢                                                                   ⁢                                  k                  y                                                      )                          =                              ∑                                          k                y                            =                                                -                                      N                    y                                                  /                2                                                                                      N                  y                                /                2                            -              1                                ⁢                                    ∑                              l                =                1                            L                        ⁢                                          n                1                                  (                  m                  )                                            ⁢                                                C                  1                                ⁡                                  (                  y                  )                                            ⁢                              p                ⁡                                  (                  y                  )                                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                           ⁢                                      k                    y                                    ⁢                  y                                                                                        (        2        )                                          S          ⁡                      (                                          k                y                            +                              m                ⁢                                                                   ⁢                Δ                ⁢                                                                   ⁢                                  k                  y                                                      )                          =                              ∑                                          k                y                            =                                                N                  y                                /                2                                                                                      N                  y                                /                2                            -              1                                ⁢                                    p              ⁡                              (                y                )                                      ⁢                          ⅇ                              ⅈ                ⁢                                                                   ⁢                                  (                                                            k                      y                                        -                                          m                      ⁢                                                                                           ⁢                      Δ                      ⁢                                                                                           ⁢                                              k                        y                                                                              )                                ⁢                y                                                                        (        3        )            wherein p(y) indicates the spin density of the image to be reconstructed along the y-axis (the x-dependency of the image was left out of consideration for reasons of clarity). The procedure in the reconstruction is schematically shown in FIG. 2, whereby a single line was reconstructed from another acquired line.
In the SMASH method, exact knowledge of the coil sensitivity distribution Cl(y) of each coil along the y-direction is required, this usually being determined via a separate registration. Due to disturbances as a result of noise and spin density fluctuations within the subject, it is usually extremely difficult to determine this. As shown in FIG. 2, an outer coil map is employed in order to determine the complex coefficients for the linear combination of each and every one of the data sets of coil l through coil L of each harmonic m (left). This enables at least one offset line to be reconstructed from a normally acquired line. At least two linear combinations are implemented, leading to two shifted data sets 23 that are combined to form a complete data set. This data set is then Fourier-transformed in order to generate the ultimate image. This image has the composite sensitivity and the signal-to-noise ratio S/N of an aggregate phase image 24.
Since, as already mentioned, it can be extremely difficult in practice to identify the coil sensitivity profiles Cl(y), Jakob et al invented the Auto-SMASH technique (Jakob P M, Griswold M A, Edelman, R R, Sodickson D K, Auto-SMASH: a self-calibrating technique for SMASH imaging. MAGMA 7:42-54 (1998)). In this technique, additional lines, referred to as “auto calibration signals” (referred to below as ACS lines) are acquired at intermediate positions in the k-space. These lines would be skipped in a SMASH acquisition. The determination of the coil weighting factors in Auto-SMASH occurs via a fit between the ACS lines and the conventionally acquired lines. The determination of the weighting factors and the reconstruction occur directly in k-space. This process can be illustrated with the following equation                                           ∑                          1              =              0                        L                    ⁢                                    n              1                              (                0                )                                      ⁢                                          S                ACS                            ⁡                              (                                                      k                    y                                    -                                      m                    ⁢                                                                                   ⁢                    Δ                    ⁢                                                                                   ⁢                                          k                      y                                                                      )                                                    =                              ∑                          1              =              0                        L                    ⁢                                    n              1                              (                m                )                                      ⁢                          S              ⁡                              (                                  k                  y                                )                                                                        (        4        )            whereby n1(m) again reference the weighting factors for coil l given a k-space offset of mΔky (see FIG. 3). In general, the weightings n1(0) of the zero-h harmonic in the above equation are arbitrary; however, these are equated with constant phase offset in most instances of a unit quantity, whereby the phase aligns the signals of each of the respective coils in the arrangement. This leads to an ultimate image with the intensity profile of an aggregate phase image.
FIG. 3 is a schematic diagram of a conventional AUTO-SMASH reconstruction (Jakob et al). Instead of an external coil map, at least one extra line 25 is acquired in addition to the normal SMASH data set. These extra lines are employed in order to determine the complex coefficients measured via a fit between the ACS lines and regularly measured lines that are required in order to generate a k-space offset of nΔky, which conventionally occurs by activating a phase encoding gradient. As in SMASH, at least two linear combinations are implemented, which lead to two shifted data sets 26. These data are then combined to form a complete data set and are subsequently Fourier-transformed in order to generate the ultimate, composite image 27. This image has the composite sensitivities and the S/N of a phase-summed image.
Whereas it has been shown that the AUTO-SMASH method functions well in some instances, it has been shown in many other instances how noise and weak coil signal degrade the AUTO-SMASH reconstruction, particularly given high acceleration factors.
Heidemann et al (Heidemann, R M, Griswold, M A, Haase A, Jakob P M, Variable Density AUTO-SMASH (VD-AUTO-SMASH), Proceedings of the Eighth Scientific Meeting of the International Society for Magnetic Resonance in Medicine (page 274 (2000)) therefore proposed an expansion of the AUTO-SMASH technique, referred to as variable density AUTO-SMASH (VD-AUTO-SMASH), wherein a few extra sets of ACS lines are sampled in addition to the required minimum set of ACS lines. It has been shown that these extra lines improve the determination of the coil weighting factors under existing noise and imprecise coil signal, since additional fit combinations can be implemented. Moreover, these extra lines can be directly integrated into the k-space. As a result, reconstructed and, consequently, error-affected lines are replaced. Given the same number of acquired lines, this leads to an often improved image quality compared to the normal AUTO-SMASH acquisition and reconstruction. The quantity referred to as artifact energy is employed as a quality feature during the further course thereof. This is the difference energy of a reconstructed image and a completely acquired reference image. The artifact energy, accordingly, is a criterion for disturbances in the image that are caused by the reconstruction. The image quality becomes better as the value of the artifact energy becomes lower. The possibility of employing additional lines for determining the coil weighting factors in AUTO-SMASH and VD-AUTO-SMASH is a significant improvement in the overall imaging efficiency compared to other PPA techniques, since no additional time is required in order to acquire separate coil maps; moreover, all additionally acquired lines can be directed integrated into the reconstructed k-space, leading to an improved image quality.
The procedure in VD-AUTO-SMASH is shown in FIG. 4: as in AUTO-SMASH, a few extra lines 28 that would be normally skipped are acquired in addition to the normal SMASH data sets. These extra lines are employed in order—by a fit between these ACS lines and regularly measured lines—to determine the complex coefficients that are needed in order to generate a k-space offset of mΔky, which conventionally occurs by activating a phase gradient. The additionally acquired fit combinations lead to an improved determination of the coil weighting factors compared to AUTO-SMASH and SMASH. As in SMASH, at least two linear combinations are generated that lead to two shifted data sets 29. Moreover, the extra lines that are acquired can be directly integrated into the reconstructed data set, which leads to an increase in the image quality. These data sets are combined to form a complete data set and are subsequently Fourier-transformed in order to generate the ultimate image. This image has the composite sensitivity and the S/N of a phase-summed image.
The additional blocks of ACS lines enable the possibility of an enhanced performance capability in the case of noise since different, additional combinations can be implemented according to Equation 4 and averaged in order to obtain more optimum weightings. Moreover, these lines can be employed in the final image reconstruction, which leads to a lower artifact energy.
In the VD-AUTO-SMASH study, an outer reduction (ORF—Outer Reduction Faction) was defined that is essentially the acceleration factor that is employed in the outer parts of the k-space. It was shown in this study that the best image quality is obtained for the highest ORF that is possible for a given imaging arrangement, meaning that a larger region of the central k-space is densely sampled. For the same number of acquired lines compared to an AUTO-SMASH acquisition resulting therefrom, this strategy leads to a lower artifact energy, i.e. to an improvement of the quality of the ultimate, reconstructed image 30.
Sodickson has recently presented an even more general presentation of SMASH that employs more then one measured line in order to reconstruct each omitted k-space line (Sodickson D K, “A Generalized Basis Approach To Spatial Encoding With Coil Arrays: SMASH-SENSE Hybrids And Improved Parallel MRI At High Accelerations”, Proceedings of the Eighth Scientific Meeting of the International Society for Magnetic Resonance in Medicine, page 273 (2000)). Sodickson showed that this more general approach—compared to the standard SMASH reconstructions —leads to a lower artifact power for higher acceleration factors as well as to a better S/N in some instances.
This most recent improvement with respect to SMASH-like reconstruction methods is referred to as generalized SMASH (G-SMASH). In this reconstruction (FIG. 5), a number of acquired lines are employed for the linear combination, in contrast to the individual acquired line as employed in the conventional SMASH acquisition. It was proposed to employ a blockwise reconstruction in the reconstruction wherein more than one normally acquired lines are employed in order to reconstruct an individual block of lines. The reconstruction then proceeds to the next block.
FIG. 5 schematically shows a generalized SMASH/SENSE hybrid reconstruction (Sodickson). As in SMASH, an external coil map is employed in order to determine the complex coefficients for the linear combinations for each of the data sets of coil l through coil L of each harmonics m by fitting the coil sensitivity profiles to the spatially harmonic profiles. In this case, however, each line is reconstructed from a block of different acquired lines instead of from an individual acquired line as in SMASH. At least two linear combinations are implemented for each block, which leads to two shifted data sets 31. These blockwise combinations are applied over the entire remaining k-space. The data are then Fourier-transformed in order to generate the ultimately composed image 32. Although this image has approximately the composite sensitivity and the S/N of a phase-summed image, the signal-to-noise ratio was capable of being improved somewhat by employing a number of lines.
A principal problem of all SMASH-like reconstructions—in addition to the termination of coil sensitivities—is that the S/N of the reconstructed image corresponds only to that of a phase-summed image, since there is no possibility of forming a square sum image. Completely reconstructed individual coil images are required for the formation of a square sum image. In addition to the inherent S/N losses, errors also arise because the k-space data of the various coils in a SMASH-typical reconstruction are combined by complex addition. In instances wherein the phases of the different coils are not exactly the same, or in instances wherein slight phase differences exist between individual noise signals and the underlying, normal signal, signal losses or even complete cancellation can be observed. For this reason, great care was applied in the previous SMASH studies to insure that the phases of the coils were identically directed before the reconstruction. The only way of measuring this phase is to implement a separate measurement of the noise correlation ratio between the coils. This method of determining the appropriate coil phases can fail in many instances, which may lead to an unsatisfactory image quality and/or to serious phase cancellation.
In summary, it can be stated that all known PPA methods known up to now have two significant disadvantages:    1. In all known SMASH/AUTO-SMASH-like PPA techniques, there is a relatively high loss in the S/N of√{square root over (number of coils)}The reconstruction of all known PPA techniques ensues by complex addition of the individual picture elements, which can lead to reconstruction artifacts (phase cancellation of anti-phase elements).